Find the moment of the force $5 i + 10 j + 16 k$ acting at the point $2 i - 7 j + 10 k$ about the point $5 i + 6 j - 10 k .$

408 i + 12 j - 135 k

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- 408 i + 148 j + 35 k

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- 31 i - 191 j + 5 k

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31 i + 191 j - 5 k

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Solution

The correct option is B $- 408 i + 148 j + 35 k$
The displacement vector
$= (5 i + 6 j - 10 k) - (2 i - 7 j + 10 k)$
$= 3 i + 13 j - 20 k$
Hence
$\to M = \to F \times \to R$
$= (5 i + 10 j + 16 k) \times (3 i + 13 j - 20 k)$
$= i (- 200 - 208) - j (- 148) + 35 k$
$= - 408 i + 148 j + 35 k$

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A = 5 i + 6 j + 5 k

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